Gu, Yonggeng; Liu, Tong A prior estimate and existence of positive solutions of semilinear elliptic equation with the third boundary value problem. (English) Zbl 1136.35379 J. Syst. Sci. Complex. 14, No. 4, 388-398 (2001). This paper deals with a priori estimate and existence of positive solution of the following equations \[ \begin{gathered} Lu= f(u)\quad\text{in }\Omega,\\ a_{ij}{\partial u\over\partial x_i}\cos(n, x_j)+\alpha u= 0\quad\text{on }\partial\Omega,\end{gathered} \]where operator \[ L= -a_{ij}(x){\partial^2\over\partial x_i\partial x_j}+ a_i(x){\partial\over\partial x_i}+ a(x) \]and nonlinear term has the form \(f(u)= u^p,\;p\in[1,{N+2\over N-2})\). Here \(\Omega\) is a bounded domain in \(\mathbb{R}^N\). Reviewer: Messoud A. Efendiev (München) Cited in 3 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B45 A priori estimates in context of PDEs 35J60 Nonlinear elliptic equations Keywords:positive solution; a priori estimate; third BVP PDFBibTeX XMLCite \textit{Y. Gu} and \textit{T. Liu}, J. Syst. Sci. Complex. 14, No. 4, 388--398 (2001; Zbl 1136.35379)